Analytical Study On The Behavior Of Partially In Lled Frames Using .

International Journal of Pure and Applied MathematicsVolume 118 No. 24 2018ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issuehttp://www.acadpubl.eu/hub/Analytical Study on The Behavior ofPartially Infilled Frames Using FiniteElement Technique by HeterogeneousModela,bSindhu Nachiar S a , Anandh S bAssistant Professor,Department of Civil Engineering,SRM University, Kattankulathur, Kancheepuram,603203, IndiaApril 11, 2018AbstractThis research examines infilled frames are the structural systems that result from the composite action betweenframe and infilling wall. In times of earthquake it has beenrecently observed that such infilled frames with larger openings for windows, ventilators, etc, called as partially infilledframes, suffer from shear failure of columns. From the survey of literature on infilled frame it is found that studies inthis area are limited. Hence an attempt is made to studyanalytically the behaviour of partially infilled frames in thiswork. The frame members are modelled with six degreesof freedom two noded beam elements, the infill is modelledwith four noded plane stress elements so as to include theheterogeneity of the wall by modelling the brick and mortarseparately. The interface is modelled as link element withparticular stiffness value.In this work an attempt is made to study the influenceof i) pattern ii) height of infilling on single storey singlebay and three storey two bay frames using finite elementtechnique. The analysis is carried out for a lateral load1

International Journal of Pure and Applied Mathematicsof 10kN at top most storey level and lateral displacement,bending moment, shear force, axial force, infill stresses areobtained.Totally 184 cases have been studied. The infilled frameis stiffer than bare frame. The increase in stiffness for fullinfill is 253% and 25% for critical case of partially infilledframe than bare frame. The infilled frame to bare framestiffness ratio is 3.5 times for full infill is 1.25 times for 14infilled frame.Key Words:Infilled frame, Heterogeneous model, Stiffness1INTRODUCTIONPartially infilled frame is a composite structure formed through thepartial interactive behaviour of the infill with the bounding framemembers under inplane lateral loads. When the infilled frame issubjected to horizontal load, the infill and the frame separate overthe region where tension occurs and remain in contact where compression occurs. Slip occurs in the compression region. Consideringslip and separation, infilled frame is simplified to be equivalent tothat of a pin-jointed frame wherein the bounding frame acts as tieand strut members and the infill acts like an inclined diagonal strutmember. The effect of this interaction reduces the lateral displacement of the frame and improves its lateral strength. The bendingmoment is reduced; hence the design becomes economical thoughthe axial force is increased.2LITERATURE SURVEYIn order to assess and to critically evaluate the research works donein infilled frames, a detail review of literature has undertaken. Theresearch on infilled frames pertaining interface characteristics andtheir effects are presented in the following sections, as follows:(i) Studies on Reinforced Concrete Partial Infilling:Ozgur Anil and Sinan Altin (2006) [1] led to the conclusion thatpartially infilled RC frames exhibited significantly higher ultimatestrength and higher initial stiffness than the bare frame (frame with2Special Issue

International Journal of Pure and Applied Mathematicsno infill). While the aspect ratio of the infill wall was increased,the lateral strength and the rigidity were increased significantly.(ii) Studies on Behaviour of Partially Infilled Frames:Goutam Mondala (2007) [4] has studied the Lateral Stiffness ofMasonry Infilled Reinforced Concrete (RC) Frames With CentralOpening. In the study, a reduction factor is proposed for effective width of diagonal strut over that of the solid infilled frameto calculate its initial stiffness when a central window opening ispresent. Seven specimens of infilled frame for which details of thespecimens and experimental results are available in the publishedliterature are considered. These include single-bay single-story tosingle-bay multi-story bare frames, infilled frames without openings, and infilled frames with central openings. These specimensare analyzed by Finite Element (FE) method using the softwareSAP 2000 Version. The present study is based on initial lateralstiffness corresponding to 10% of the lateral strength of the infilledframes. Based on the comparison between initial lateral stiffnessusing FE method and from experimental initial lateral stiffness itis found that best match with experimental results are obtainedwhen (a) separation between the frame and the infill at the nonloaded diagonal is included, (b) end-offsets of beam-column jointsin RC frames is assumed to be semi rigid wherein quarter columndepth along beam from center line of column and quarter beamdepth along column from center line of beam are considered rigid,(c) the FE model is based on cracked flexural rigidity of beams andcolumns where the flexural rigidity of beam and column in tensionis taken as 0.5 Ec Ig and that of column in compression is taken as0.7 Ec Ig.3RESEARCH SIGNIFICANCEFrom the literature review it is found that only limited work hasbeen done in the area of partially infilled frame related to the influence of interface characteristics and modelling of infill element. Thepresent investigation tries to add more information in this area byconsidering the effect of infill as heterogenous plane stress models.From the studies of recent earthquakes it is found that the column adjoining infill with partial opening for ventilator or window3Special Issue

International Journal of Pure and Applied Mathematicsundergoes a severe shear failure as indicated in the Figure 1.4OBJECTIVE AND SCOPE OF THEPRESENT INVESTIGATIONThe proposed investigations are mainly aimed to analytically investigate the effect of height of infill on the behaviour of reinforcedconcrete infilled frames.a) Pattern and partial infilling used for Analytical Investigation:The pattern used for for the study is a two bay (b1,b2) threestorey(s1,s2,s3) frame which is shown in the Figure 2.Figure 2 Pattern of frameVarying partial infilling is tried on all the 3 storey and 2 bay.No of trials considered for the analysis is 184 (cases) and typicaltypes of infilled models are shown in the Figure 3.b) Details of Analytical Investigation:In this one eighty four models are considered that include M5to M8 as bare frame, 1/4th infill, 3/4th infill and full infill. M9 to4Special Issue

International Journal of Pure and Applied MathematicsM189 are various other combinations of varying heights of infill. Astandard finite element software package SAP 2000, Version 11 isused. The frame members are modeled with two noded, six degreesof freedom beam elements. For modeling the infill, heterogeneity ofthe brick masonry is represented by taking four noded plane stresselements separately for brick and mortar. The interface is modeledby link elements having three degrees of freedom on frame side andtwo degrees of freedom on infill element. The details of frame ispresented in Table 1Table 1 Details of Frame Considered for AnalysisThe parameters considered for study are modulus of elasticity,Poissons ratio,compressive strength and modulus of elasticity of theframe and infill material. The properties of materials considered foranalysis are as follows. The properties of materials considered foranalysis are given in Table 2.Table 2 Properties of Materials Used For Analysis5RESULTSi)Convergence Study8 8 mesh is considered for the full infill condition. Similarly2 2 mesh for 14 h infill, 4 4 mesh for 12 h infill, 6 6 mesh for 34 h5Special Issue

International Journal of Pure and Applied Mathematicsinfill for all the trials of analysis of partial infilled frame, from theconvergence studies made.ii)Analytical ResultsThe Tables 3 represents the comparisons of results of stiffnessobtained from analysis investigations.Table 3 Effect of Stiffness for model frameiii) Percentage Increase in Lateral StiffnessThe Percentage increase in lateral stiffness for varying infillheights for different models is shown in the Figure 4.Figure 4 Percentage increase of lateral stiffness withvarying infill heightsiv) Effect of Presence of Infill on Lateral Stiffness PredictionThe effect of presence of infill on lateral stiffness is predictedand shown in the Figure 5.Figure 5 Percentage increase of lateral stiffness6Special Issue

International Journal of Pure and Applied Mathematicsvi) Critical Values for Single Bay Single Storey and TwoBay Three Storey FrameBased on the analytical results obtained the critical values areidentified and shown in Table 4 and Table 5.Figure 6 Effect of model on lateral stiffnessvi) Critical Values for Single Bay Single Storey and TwoBay Three Storey FrameBased on the analytical results obtained the critical values areidentified and shown in Table 4 and Table 5.Table 4 Critical values for single bay single storey frame7Special Issue

International Journal of Pure and Applied MathematicsSpecial IssueTable 5 Critical values for two bay three storey frameM 53 B1B2bay, s20.75hremain0h M 98 B1bayonly, s20.75hremain1hM 58B1B2bay, s11hremain0.75h M 166 B2bayonly, s10.75hremain1hM 85 B1bayonly, s11hremain0h M 178 B2bayonly, s11hremain0.75h6DISCUSSIONSi) Effect of partial infilling? The maximum stiffness is achieved in full infill of 1.35 times instrut model, 7.12 times in plane stress model and 1.67 timesin heterogenous model of bare frame? The maximum axial force ( ve) is resulted on full infill of1.65 times in strut model, 1.34 times in plane stress modeland 1.68 times in heterogenous model of bare frame.th? The maximum axial force (-ve) is resulted on 41 model of0.99 times in strut model, 1.02 times in plane stress modeland 1.30 times in heterogenous model of bare frame.? The maximum shear force ( ve) is resulted on th model ofth1.101 times in strut model, 41 model 1.305 times in plane8

International Journal of Pure and Applied MathematicsSpecial Issuestress model and 1.648 times in heterogenous model of bareframe.? The maximum shear force (-ve) is resulted on full infill ofth3.714 times in strut model, 12 model is 1.537 times in planestress model and 3.374 times in heterogenous model of bareframe.th? The maximum bending moment ( ve) is resulted on 14 modelof 1 times in strut model, 0.6 times in plane stress model and0.88 times in heterogenous model of bare frame.th? The maximum bending moment (-ve) is resulted on 14 modelof 0.996 times in strut model, 1.012 times in plane stressmodel and 1.23 times in heterogenous model of bare frame.th? The 14 model is critical in ve axial force, ve shear force andth( ) & (-) ve bending moment .so the partially is tried in 14(H) model.ii) Pattern of Variation of Various Quantities for Critical Case Based on Less Lateral Stiffness and MaximumShear Force The suggested equations for the variation of various quantitiesfor critical case based on Less Lateral Stiffness from the graph ofinfill height vs the corresponding parameters areStiffness 25.86h3 - 44.3h2 24.98h 6.024AF (-ve) -78.96h3 109.1h2 - 11.53h 55.84AF ( ve) -4.693h3 7.44h2 - 9.566h 8.1Smin -246.3h3 336.3h2 - 67.63h 13.6Smax -51.62h3 81.68h2 - 8.913h 10.1SF (-ve) -306.7h3 398.2h2 - 75.52h 0.22SF ( ve) -780.8h3 1123h2 - 341.1h 8.16BM (-ve) -13784h3 25164h2 - 11650h 6567BM ( ve) -3513h3 6601h2 - 4872h 7278 The suggested equations for the variation of various quantitiesfor critical case based on Maximum Shear Force from the graph ofinfill height vs the corresponding parameters areStiffness -6.551h3 6.189h2 5.679h 8.196AF (-ve) -15.84h3 23.16h2 3.32h 55.449